Answered: Given the following integral SV2-25 ox…

Given the following integral SV2-25 ox Determine the Trigonometric Substitution formulas that need to be used for this integral.

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter4: Nonlinear Oscillations And Chaos

Section: Chapter Questions

Problem 4.14P

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Concept explainers

Newton’s Third Law of Motion

The horse pulls the cart and the cart pulls the horse in response as per Newton third law. So the big question is, “Don’t the two forces cancel each other? How does the cart accelerate?”

Question

Expert Solution

Step 1

The given integral is:

$I = \int \sqrt{x^{2} - 25} d x$

Trigonometric relation used is:

$\tan^{2} x + s e c^{2} y = 1$

The given integral is easy to solve by trigonometric substitution:

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